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Electronic and Optical Properties of Conjugated Polymers (International Series of Monographs on Physics) by William Barford (2005)

Conjugated polymers have important technological applications, including solar cells and light emitting displays. They are also active components in many biological processes. In recent years, there have been significant advances in our understanding of these systems, owing to both improved experimental measurements and the development of advanced computational techniques. The aim of this book is to describe and explain the electronic and optical properties of conjugated polymers. It focuses on the character and energetic ordering of the electronic states and relates these properties to experimental observations in real systems.

CONTENTS

1 Introduction to conjugated polymers 1

2 π-electron theories of conjugated polymers 7

2.1 Introduction 7

2.2 The many body Hamiltonian 7

2.3 The Born-Oppenheimer approximation 8

2.4 Second quantization of the Born-Oppenheimer

Hamiltonian 10

2.5 spn hybridization 11

2.5.1 sp hybridization 12

2.5.2 sp2 hybridization 12

2.5.3 sp3 hybridization 14

2.5.4 Remarks 14

2.6 π-electron models 15

2.7 Electron-phonon coupling 17

2.7.1 The nuclear-nuclear potential, Vn({un}) 18

2.8 Summary of π-electron models 19

2.8.1 The H¨uckel model 19

2.8.2 The Su-Schrieffer-Heeger model 20

2.8.3 The Pariser-Parr-Pople model 20

2.9 Symmetries and quantum numbers 21

2.9.1 Spatial symmetries 22

2.9.2 Particle-hole symmetry 22

2.9.3 Quantum numbers 24

2.9.4 State labels 24

3 Noninteracting electrons 26

3.1 Introduction 26

3.2 The noninteracting (H¨uckel) Hamiltonian 26

3.3 Undimerized chains 26

3.3.1 Cyclic chains 26

3.3.2 Linear chains 29

3.4 Dimerized chains 29

3.4.1 Cyclic chains 30

3.4.2 Linear chains 32

3.5 The ground state and particle-hole excitations 32

3.5.1 The band, charge, and spin gaps 34

3.6 Symmetries 35

3.6.1 Particle-hole symmetry and particle-hole parity 35

3.6.2 Linear chains and inversion symmetry 37

4 Electron-lattice coupling I: Noninteracting electrons 39

4.1 Introduction 39

4.2 The Peierls model 39

4.3 The dimerized ground state 41

4.3.1 The H¨uckel ‘4n + 2’ rule 43

4.4 Self-consistent equations for {∆n} 43

4.5 Solitons 45

4.5.1 Odd-site chains 45

4.5.2 Even-site chains 47

4.6 Soliton-antisoliton pair production 49

4.7 Polarons 52

4.8 Nondegenerate systems 52

4.9 The continuum limit of the Su-Schrieffer-Heeger model 55

4.10 Dynamics of the Su-Schrieffer-Heeger model 57

4.11 Self-trapping 57

4.12 Concluding remarks 58

5 Interacting electrons 59

5.1 Introduction 59

5.1.1 Broken symmetries 59

5.1.2 Undimerized chains 60

5.1.3 Dimerized chains 62

5.2 The weak-coupling limit 64

5.2.1 Undimerized chains 64

5.2.2 Dimerized chains 64

5.3 The strong-coupling limit 65

5.3.1 Low-energy dimerized Heisenberg

antiferromagnet 65

5.3.2 High-energy spinless fermion model 66

5.4 The phase diagram of the undoped Pariser-Parr-Pople

model 69

5.5 The valence bond method 69

6 Excitons in conjugated polymers 73

6.1 Introduction 73

6.2 The weak-coupling limit 74

6.2.1 The effective-particle model 74

6.2.2 Solutions of the effective-particle model 79

6.2.3 Comparisons to the numerical calculations 79

6.2.4 Refinements of the theory 85

6.3 The strong-coupling limit 86

6.3.1 The effective-particle model 87

6.4 The intermediate-coupling regime 90

6.5 Concluding remarks 92

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